Khinchin’s inequality,Dunford-Pettis and compact operators on the space <Emphasis Type="Italic">C</Emphasis>([0, 1], <Emphasis Type="Italic">X</Emphasis>)

We prove that if X, Y are Banach spaces, Ω a compact Hausdorff space and U:C(Ω, X) → Y is a bounded linear operator, and if U is a Dunford-Pettis operator the range of the representing measure G(Σ) ? DP(X, Y) is an uniformly Dunford-Pettis family of operators and ∥G∥ is continuous at Ø. As applications of this result we give necessary and/or sufficient conditions that some bounded linear operators on the space C([0, 1], X) with values in c ₀ or l _p, (1 ≤ p < ∞) be Dunford-Pettis and/or compact operators, in which, Khinchin’s inequality plays an important role.     

Some limit relations in the A1 tableau of Dunkl-Cherednik operators

In this paper we study some limit relations involving some q-special functions related with the A₁ (root system) tableau of Dunkl-Cherednik operators. Concretely we consider the limits involving the nonsymmetric q-ultraspherical polynomials (q-Rogers polynomials), ultraspherical polynomials (Gegenbauer polynomials), q-Hermite and Hermite polynomials.     

On K0-groups of operator algebras on Banach spaces

This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K ₀(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X ² is not a sufficient condition of K ₀(B(X)) = 0.     

Fourier Transforms of Bounded Bilinear Forms on C＊（S1）×C＊（S2） of Foundation ＊-semigroups S1 and S2

The author gives a characterization of the Fourier transforms of bounded bilinear forms on C＊（S1）×C＊（S2） of two foundation semigroups S1 and S2 in terms of Jordan ＊-representations, hemimogeneous random fields, and as well as weakly harmonizable random fields of S1 and S2 into Hilbert spaces.     

Differential-geometric Newton method for the best rank-(R1, R2, R3) approximation of tensors

An increasing number of applications are based on the manipulation of higher-order tensors. In this paper, we derive a differential-geometric Newton method for computing the best rank-(R ₁, R ₂, R ₃) approximation of a third-order tensor. The generalization to tensors of order higher than three is straightforward. We illustrate the fast quadratic convergence of the algorithm in a neighborhood of the solution and compare it with the known higher-order orthogonal iteration (De Lathauwer et al., SIAM J Matrix Anal Appl 21(4):1324–1342, 2000). This kind of algorithms are useful for many problems. This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its authors. Research supported by: (1) Research Council K.U.Leuven: GOA-Ambiorics, CoE EF/05/006 Optimization in Engineering (OPTEC), (2) F.W.O.: (a) project G.0321.06, (b) Research Communities ICCoS, ANMMM and MLDM, (3) the Belgian Federal Science Policy Office: IUAP P6/04 (DYSCO, “Dynamical systems, control and optimization”, 2007–2011), (4) EU: ERNSI. M. Ishteva is supported by a K.U.Leuven doctoral scholarship (OE/06/25, OE/07/17, OE/08/007), L. De Lathauwer is supported by “Impulsfinanciering Campus Kortrijk (2007–2012)(CIF1)” and STRT1/08/023.     

Lp-Approximable Sequences of Vectors and Limit Distribution of Quadratic Forms of Random Variables

The properties of L₂-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are “two-wing” averages of martingale differences. The results constitute the first significant advancement in the theory of L₂-approximable sequences since 1976 when Moussatat introduced a narrower notion of L₂-generated sequences. The method relies on a study of certain linear operators in the spaces L_p and l_p. A criterion of L_p-approximability is given. The results are new even when the weight generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method.     

A special identity between three 2F1(a,b;c;4) hypergeometric series

As a by-product of the calculation of eigenvalues of a particular SO(3) invariant operator in the enveloping algebra of SO(5), a three terms relation between three hypergeometric series emerges.     

Note on theK0 of rings with Zariskian filtration

For a noncommutative Zariski ringR with associated graded ringG(R) of finite global dimension there is an injectionK _o(R) K _o (G(R)). The result applies to certain rings of differential operators, in particular to the ring of germs of microlocal differential operators that also provides an example of a nonpositively filtered Zariski ring.Research fellow at UIA, supported by a grant from the Province of Antwerp.Supported by an NFWO grant.     

An Averaging Method for Singularly Perturbed Systems of Semilinear Differential Inclusions with C0-Semigroups

We consider a system of two semilinear differential inclusions with infinitesimal generators of C ₀-semigroups. The nonlinear terms are of high frequency with respect to time and periodic with a specified period. Moreover, they are condensing in the state variables (x,y) with respect to a suitable measure of noncompactness. The goal of the paper is to give sufficient conditions to guarantee, for >0 sufficiently small, the existence of periodic solutions and to study their behaviour as 0. The main tool to achieve this is the topological degree theory for uppersemicontinuous, condensing vector fields.     

Stokes型积分-微分方程Q_2-P_1元的超收敛分析

本文研究Q2-P1混合元对Stokes型积分-微分方程的有限元方法.利用积分恒等式技巧给出了关于流体速度u和压力p的误差估计,特别是在压力p的误差中去掉了影响解的稳定性的1因子t-2,改善了以往文献的结果.同时,通过构造适当的插值后处理算子得到了整体超收敛结果.     

The isometric extension of the into mapping from the unit sphere S 1( E ) to S 1( l ∞(Γ))

This paper considers the isometric extension problem concerning the mapping from the unit sphere S ₁(E) of the normed space E into the unit sphere S ₁(l ^∞(Γ)). We find a condition under which an isometry from S ₁(E) into S ₁(l ^∞(Γ)) can be linearly and isometrically extended to the whole space. Since l ^∞(Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are solved. More precisely, if E and F are two normed spaces, and if V ₀: S ₁(E) → S ₁(F) is a surjective isometry, where c ₀₀(Γ) ⊆ F ⊆ l ^∞(Γ), then V ₀ can be extended to be an isometric operator defined on the whole space. This work is supported by Natural Science Foundation of Guangdong Province, China (Grant No. 7300614)     

Semigroups of linear operators on p-Fréchet spaces, 0 < p < 1

We develop the beginning of a theory of semigroups of linear operators on p-Fréchet spaces, 0 < p < 1 (which are non-locally convex F-spaces), and give some applications.     

K2 of a Ring via the G-Construction

We interpret the Steinberg symbols x_i,j(a) as homotopies contracting the elementary matrices e_i,j(a), the latters being represented by certain arcs in a simplicial model of the K-theory. We further prove the Steinberg relations for these homotopies. This provides an explicit map from K₂ of a ring, defined classically as ker(St(R) → GL(R)), to π₂ of the G-construction assigned to R. Though the two groups are known to be isomorphic, a certain work is to be done to prove that this explicit map is an isomorphism. Mathematics Subject Classification 1991: Primary 19B99, 19D99; secondary 18E10, 18F25.     

A short proof of w1n (Hom(C2r+1, Kn+2)) = 0 for all n and A graph colouring theorem by Babson and Kozlov

We show that the n-th power of the first Stiefel-Whitney class of the ℤ₂-action on the graph complex Hom(C _2r+1, K _n+2) is zero, confirming a conjecture by Babson and Kozlov. This yields a considerably simplified proof of their graph colouring theorem, which is also known as the Lovsz conjecture. This research was supported by the Deutsche Forschungsgemeinschaft within the European graduate program “ Combinatorics, Geometry, and Computation” (No. GRK 588/2)     

On the ideal structure of some Banach algebras related to convolution operators on L(G)

Let G be a locally compact group and let p∈(1,∞). Let be any of the Banach spaces C_δ,p(G), PF_p(G), M_p(G), AP_p(G), WAP_p(G), UC_p(G), PM_p(G), of convolution operators on L^p(G). It is shown that PF_p(G)′ can be isometrically embedded into UC_p(G)′. The structure of maximal regular ideals of (and of MA_p(G)″, B_p(G)″, W_p(G)″) is studied. Among other things it is shown that every maximal regular left (right, two sided) ideal in is either dense or is the annihilator of a unique element in the spectrum of A_p(G). Minimal ideals of is also studied. It is shown that a left ideal M in is minimal if and only if , where Ψ is either a right annihilator of or is a topologically x-invariant element (for some x∈G). Some results on minimal right ideals are also given.     

Extension of Finite Rank Operators and Operator Ideals with the Property (I)

We present criteria and related techniques which help to decide whether the adjoint operator ideal (𝔄*, A *) of an injective and totally accessible maximal Banach ideal (𝔄, A ) is itself also totally accessible. This approach (which involves the transfer of the principle of local reflexivity to operator ideals) is based on the extension of finite rank operators, viewed as elements of the adjoint ideal (𝔄*, A *). Using the local properties (I) and (S) of the corresponding product ideal 𝔄* ∘ 𝔏_∞, these methods even enable us to show that 𝔏_∞ and 𝔏₁ cannot be totally accessible – answering an open question of Defant and Floret .     

Isometric weighted composition operators on weighted Banach spaces of type

We characterize those weighted composition operators on weighted Banach spaces of holomorphic functions of type which are an isometry.

     

A Classification of Regular p-Groups with Invariants (e, 2, 1)

The class of the regular p-groups is one of the important classes in p-groups. Not only it has many similar properties as abelian p-groups, but also many of the p-groups belong to this class. In this paper, using the algorithms for determining the isomorphic regular p-groups, we give a complete classification of the regular p-groups with e-invariants (e, 2, 1).Supported by SXYSF 991003.     

The Local Index Formula for SU q (2)

We discuss the local index formula of Connes–Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula. (Received: January 2005)